In this thesis, we propose a hierarchical control architecture for voltage in power distribution networks where there is a separation between the slow time-scale, in which the settings of conventional voltage regulation devices are adjusted, and the fast time-scale, in which voltage regulation through active/reactive power injection shaping is accomplished. Slow time-scale devices will generally be existing hardware, e.g., voltage regulation transformers, which will be dispatched at appropriate time intervals to reduce the wear on their mechanical parts. In contrast, fast time-scale devices are considered to be devices that connect to the grid through power electronics, e.g., photovoltaic (PV) installations.
In the slow time-scale control, we propose a method to optimally set the tap position of voltage regulation transformers. We formulate a rank-constrained semidefinite program (SDP), which is then relaxed to obtain a convex optimization that is solved distributively with the Alternating-Direction Method of Multipliers (ADMM). In the fast time-scale control, we propose the following schemes: (i) a feedback-based approach to regulate system voltages, and (ii) an optimization-based approach that maintains the desired operating state through a quadratic program developed from a linear distribution system model.
Finally, we showcase the operation of the two time-scale control architecture in an unbalanced three-phase distribution system. The test system in the case studies is derived from the IEEE 123-bus test system and has a high penetration of residential PV installations and electric vehicles (EVs). We provide several examples that demonstrate the interaction between the two time-scales and the impact of the proposed control on component behaviors.